Sometimes I use my wifes '16 1500 chevy crew cab 4wd 5.3 engine 6L80 tranny 3.42 gears to pull a 20' 12k gvwr car hauler with a tractor with a cab = around 11.5' tall. Total weight is around 8k-9k depending what implements are on the tractor. I can load the tractor to stay within the trucks rawr so no weight carrying issues.
The truck does ok in the flat country but in the hills and in high head wind it really works hard. I wouldn't want to make a vacation pulling that much weight with the 5.3 smallblock. Now if your truck had the optional 6.2 engine at 420hp/460 torque with the 3.73 gears then no issues.
A 3/4 ton gas or diesel would make a much better towing platform to go anywhere for that size trailer.